

A268810


a(n) = 2*floor(3*n*(n+1)/4).


1



0, 2, 8, 18, 30, 44, 62, 84, 108, 134, 164, 198, 234, 272, 314, 360, 408, 458, 512, 570, 630, 692, 758, 828, 900, 974, 1052, 1134, 1218, 1304, 1394, 1488, 1584, 1682, 1784, 1890, 1998, 2108, 2222, 2340, 2460, 2582, 2708, 2838, 2970, 3104, 3242, 3384, 3528, 3674, 3824, 3978, 4134, 4292
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,2


LINKS

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (3,4,4,3,1).


FORMULA

a(n) = (3*n^2  3*n + cos(n*Pi/2) + sin(n*Pi/2)  1)/2.
a(n) = A268428(n)  149.
a(n) = (1/4+i/4)*((i1)+(i)^ni*i^n(3*i+3)*n+(3*i+3)*n^2), where i is the imaginary unit.
a(n) = (3*n^2  3*n + (1)^binomial(n+1,2)  1)/2.
G.f.: (2*(x^3 + x^2 + x)/((1  x)^3*(x^2 + 1))).


MATHEMATICA

Table[2 Floor[3 n (n + 1)/4], {n, 0, 60}]
LinearRecurrence[{3, 4, 4, 3, 1}, {0, 2, 8, 18, 30}, 60]


PROG

(MAGMA) [2*Floor(3*n*(n+1)/4): n in [0..60]]; // Vincenzo Librandi, Feb 15 2016
(PARI) vector(60, n, n; 2*floor(3*n*(n+1)/4)) \\ G. C. Greubel, Nov 04 2018


CROSSREFS

Cf. A087960, A268428.
Sequence in context: A295522 A065131 A192157 * A063581 A293296 A055044
Adjacent sequences: A268807 A268808 A268809 * A268811 A268812 A268813


KEYWORD

nonn,easy


AUTHOR

Mikk Heidemaa, Feb 13 2016


STATUS

approved



